Meriam, Kraige & Bolton — Kinetics of Particles: Problem 3_267

3/267 A person rolls a small ball with speed $u$ along the floor from point $A$. If $x = 3R$, determine the required speed $u$ so that the ball returns to $A$ after rolling on the circular surface in the vertical plane from $B$ to $C$ and becoming a projectile at $C$. What is the minimum value of $x$ for which the game could be played if contact must be maintained to point $C$? Neglect friction.